Two econometric applications illustrate
the use of implicit copula models with non-Gaussian data.
The first is a time-varying heteroscedastic time series model for U.S. inflation
between 1954:Q1 and 2020:Q2. The implicit copula is a copula process
constructed from
a nonlinear state space model as in [1]}. It is a
“time series copula” that captures serial dependence.
The second application is a five factor asset pricing regression model [2]}
with an asymmetric Laplace marginal distribution for monthly equity
returns. The implicit copula here is a “regression copula” process with respect to the covariates as in [3]}.
The copula model forms
a distributional regression [4]}, [5]}, where the five factors affect the entire distribution
of equity returns, not just its first or other moments.
In both applications the implicit copulas are of dimension equal to the number of
observations, so that they are high-dimensional. Nevertheless, their auxiliary representation allows for likelihood-based estimation of the copula parameters.
In both examples the marginal distribution of the response variables exhibit strong asymmetries.
